Centre Court watched nervously as Fery twice fought back from a break down in the fourth set to stun Dimitrov 7-5 3-6 4-6 6-4 7-6 (10-7), ending on a tiebreak.
Many had expected former world number three Dimitrov to come out on top, against Fery, who got his place in the competition as a wildcard.
Wildcard places are extra spots given to players who did not qualify automatically for a tennis tournament.
Places are often awarded to players based on their previous performances at Wimbledon, or to increase British participation in the competition – but only once has a wildcard gone on to lift the Wimbledon trophy.